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Identifiability issues of age–period and age–period–cohort models of the Lee–Carter type

Beutner, Eric; Reese, Simon LU and Urbain, Jean-Pierre (2017) In Insurance: Mathematics and Economics 75. p.117-125
Abstract

The predominant way of modelling mortality rates is the Lee–Carter model and its many extensions. The Lee–Carter model and its many extensions use a latent process to forecast. These models are estimated using a two-step procedure that causes an inconsistent view on the latent variable. This paper considers identifiability issues of these models from a perspective that acknowledges the latent variable as a stochastic process from the beginning. We call this perspective the plug-in age–period or plug-in age–period–cohort model. Defining a parameter vector that includes the underlying parameters of this process rather than its realizations, we investigate whether the expected values and covariances of the plug-in Lee–Carter models are... (More)

The predominant way of modelling mortality rates is the Lee–Carter model and its many extensions. The Lee–Carter model and its many extensions use a latent process to forecast. These models are estimated using a two-step procedure that causes an inconsistent view on the latent variable. This paper considers identifiability issues of these models from a perspective that acknowledges the latent variable as a stochastic process from the beginning. We call this perspective the plug-in age–period or plug-in age–period–cohort model. Defining a parameter vector that includes the underlying parameters of this process rather than its realizations, we investigate whether the expected values and covariances of the plug-in Lee–Carter models are identifiable. It will be seen, for example, that even if in both steps of the estimation procedure we have identifiability in a certain sense it does not necessarily carry over to the plug-in models.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Age–period model, Age–period–cohort model, Identifiability, Lee–Carter model, Plug-in Lee–Carter model, Time series model
in
Insurance: Mathematics and Economics
volume
75
pages
9 pages
publisher
Elsevier
external identifiers
  • scopus:85020425752
  • wos:000406983200011
ISSN
0167-6687
DOI
10.1016/j.insmatheco.2017.04.006
language
English
LU publication?
yes
id
972206cc-0aa1-4b5c-92a0-8aaf9a647326
date added to LUP
2017-06-26 14:23:14
date last changed
2017-09-18 11:42:43
@article{972206cc-0aa1-4b5c-92a0-8aaf9a647326,
  abstract     = {<p>The predominant way of modelling mortality rates is the Lee–Carter model and its many extensions. The Lee–Carter model and its many extensions use a latent process to forecast. These models are estimated using a two-step procedure that causes an inconsistent view on the latent variable. This paper considers identifiability issues of these models from a perspective that acknowledges the latent variable as a stochastic process from the beginning. We call this perspective the plug-in age–period or plug-in age–period–cohort model. Defining a parameter vector that includes the underlying parameters of this process rather than its realizations, we investigate whether the expected values and covariances of the plug-in Lee–Carter models are identifiable. It will be seen, for example, that even if in both steps of the estimation procedure we have identifiability in a certain sense it does not necessarily carry over to the plug-in models.</p>},
  author       = {Beutner, Eric and Reese, Simon and Urbain, Jean-Pierre},
  issn         = {0167-6687},
  keyword      = {Age–period model,Age–period–cohort model,Identifiability,Lee–Carter model,Plug-in Lee–Carter model,Time series model},
  language     = {eng},
  month        = {07},
  pages        = {117--125},
  publisher    = {Elsevier},
  series       = {Insurance: Mathematics and Economics},
  title        = {Identifiability issues of age–period and age–period–cohort models of the Lee–Carter type},
  url          = {http://dx.doi.org/10.1016/j.insmatheco.2017.04.006},
  volume       = {75},
  year         = {2017},
}